# Anti-unification in Constraint Logic Programming

## TL;DR

This paper explores anti-unification in Constraint Logic Programming, defining the problem, proving its NP-completeness, and proposing a polynomial-time algorithm that produces acceptable generalizations efficiently.

## Contribution

It introduces a novel anti-unification algorithm for CLP goals, balancing computational complexity with practical effectiveness.

## Key findings

- Anti-unification in CLP is NP-complete.
- Proposed algorithm computes well-defined generalizations efficiently.
- Initial experiments show acceptable generalizations with naive implementation.

## Abstract

Anti-unification refers to the process of generalizing two (or more) goals into a single, more general, goal that captures some of the structure that is common to all initial goals. In general one is typically interested in computing what is often called a most specific generalization, that is a generalization that captures a maximal amount of shared structure. In this work we address the problem of anti-unification in CLP, where goals can be seen as unordered sets of atoms and/or constraints. We show that while the concept of a most specific generalization can easily be defined in this context, computing it becomes an NP-complete problem. We subsequently introduce a generalization algorithm that computes a well-defined abstraction whose computation can be bound to a polynomial execution time. Initial experiments show that even a naive implementation of our algorithm produces acceptable generalizations in an efficient way. Under consideration for acceptance in TPLP.